On Field Size and Success Probability in Network Coding

  • Authors:
  • Olav Geil;Ryutaroh Matsumoto;Casper Thomsen

  • Affiliations:
  • Department of Mathematical Sciences, Aalborg University, Denmark;Department of Communications and Integrated Systems, Tokyo Institute of Technology, Japan;Department of Mathematical Sciences, Aalborg University, Denmark

  • Venue:
  • WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
  • Year:
  • 2008

Quantified Score

Hi-index 0.00

Visualization

Abstract

Using tools from algebraic geometry and Gröbner basis theory we solve two problems in network coding. First we present a method to determine the smallest field size for which linear network coding is feasible. Second we derive improved estimates on the success probability of random linear network coding. These estimates take into account which monomials occur in the support of the determinant of the product of Edmonds matrices. Therefore we finally investigate which monomials can occur in the determinant of the Edmonds matrix.